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Simplifying 10x3 + 9x2 + -18x = 0 Reorder the terms: -18x + 9x2 + 10x3 = 0 Solving -18x + 9x2 + 10x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-18 + 9x + 10x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-18 + 9x + 10x2)' equal to zero and attempt to solve: Simplifying -18 + 9x + 10x2 = 0 Solving -18 + 9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.8 + 0.9x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.9x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.9x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.9x + x2 = 0 + 1.8 0.9x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.9x + x2 = 1.8 The x term is 0.9x. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9x + 0.2025 + x2 = 1.8 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = 1.8 + 0.2025 Combine like terms: 1.8 + 0.2025 = 2.0025 0.2025 + 0.9x + x2 = 2.0025 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 2.0025 Calculate the square root of the right side: 1.41509717 Break this problem into two subproblems by setting (x + 0.45) equal to 1.41509717 and -1.41509717.Subproblem 1
x + 0.45 = 1.41509717 Simplifying x + 0.45 = 1.41509717 Reorder the terms: 0.45 + x = 1.41509717 Solving 0.45 + x = 1.41509717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 1.41509717 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 1.41509717 + -0.45 x = 1.41509717 + -0.45 Combine like terms: 1.41509717 + -0.45 = 0.96509717 x = 0.96509717 Simplifying x = 0.96509717Subproblem 2
x + 0.45 = -1.41509717 Simplifying x + 0.45 = -1.41509717 Reorder the terms: 0.45 + x = -1.41509717 Solving 0.45 + x = -1.41509717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -1.41509717 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -1.41509717 + -0.45 x = -1.41509717 + -0.45 Combine like terms: -1.41509717 + -0.45 = -1.86509717 x = -1.86509717 Simplifying x = -1.86509717Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96509717, -1.86509717}Solution
x = {0, 0.96509717, -1.86509717}
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